Both the CEMA and MHEA belt conveyor handbooks give methods of determining the discharge trajectory from trough belt conveyors. Other publications may also give this information. ■

The CEMA formulas are based on velocity and gravity. You also need to know the surcharge angle of the conveyed material as it too plays a factor.

Here is a little spreadsheet that I put together from the formulas in CEMA.

Attachments

trajectory (ZIP)

■

Originally Posted by Lyle Brown

https://forum.bulk-online.com/showth...threadid=10542

Post no. 13 in this thread was never answered ■

Good morning Saini..

Firstly, good luck with a conveyor at 18 degrees.

(I sincerely hope you do not transport large round shaped lumps with no fines on your belt)

Secondly, simply use Issac Newton's good old laws of motion to calculate and plot the trajectory(s)

v^2= u^2 + 2 x a x s

s= u x t + .5 x a x t^2

Thirdly, at such slow speeds, remember that the material on top has slightly further to go around the pulley than the material next to the belt, so it leaves the conveyor at a slightly higher speed, and has a flatter trajectory

Fourth point is that if the material is sticky, it will have a more vertical trajectory, and..

Last point is that if your terminal pulley is above the belt line to assist in the transition length, then the discharge angle will be your 18 degrees plus the transition angle (this makes a big difference, especially at higher speeds)

Cheers

LSL Tekpro ■

Shri Puneet Saini,

There are well established methods for calculating material trajectory at discharge pulley of belt conveyors. It is not possible to narrate the exact formulae here. You can refer to relevant literature.

The basic considerations are that if belt speed is sufficiently high in relation to pulley diameter, then material will simply get thrown out at the point where belt touches the pulley periphery. If this is not so, then material will remain on belt till it traverses certain angular distance and then it separates out from the belt. Once the material has separated from the belt it follows the universal laws of motion i.e. it is being thrown out at certain velocity and direction and then it is falling freely under influence of gravity (of earth).

The material will separate out from belt immediately at the point of entry, if v square upon gr is equal or greater than one. In case it is less than one, then it will separate at angle A from horizontal line from pulley centre wherein sinA = v square upon gr where g is acceleration due to gravity and r is pulley radius.

There are certain finer aspects being adopted by few methods, but above is the basic method. Generally air resistance is ignored unless you are throwing at a very high velocity and or at a very great depth.

Ishwar Mulani

Author of book : Engineering Science and Application Design for Belt Conveyors

Author of book : Belt Feeder Design and Hopper Bin Silo

Tel. No. : 0091 (0)20 2587 1916

Email : parimul@pn2.vsnl.net.in ■

Originally Posted by Graham Spriggs

Thirdly, at such slow speeds, remember that the material on top has slightly further to go around the pulley than the material next to the belt, so it leaves the conveyor at a slightly higher speed, and has a flatter trajectory

Cheers

LSL Tekpro

Whence the acceleration?...but we know what you're getting at.

Discharge is too complex to tie down. As the material stream negotiates the transition it climbs a litle bit steeper as Graham says. During this final climb the cross section is trying to change from a trapezium with a supplanted sector to a final single sector. (According to most learned texts on the subject) This involves some lateral displacement of some lumps and the principle of the conservation of energy suggests that those lumps that move sidewards must therefore slow down forwards. Gravity is arguably the sole force in play and it would take some fancy sums to determine if the acceleration imparted to the sidestepping lump, during descent, was sufficient to maintain the forward velocity. Who knows? Sticky stuff is also important because then the change in cross section will not be so much in evidence and the material will jump off the belt more akin to the book recommendations. ■

Originally Posted by louispanjang

"Whence the acceleration?...but we know what you're getting at...."

"This involves some lateral displacement of some lumps and the principle of the conservation of energy suggests that those lumps that move sidewards must therefore slow down forwards. Gravity is arguably the sole force in play and it would take some fancy sums to determine if the acceleration imparted to the sidestepping lump."

"Whence the acceleration?"..... well, the material rounding the pulley tends to shear as it has a further to travel round the outside. The shear force accellerates the outer material a bit, with the energy coming from the conveyor belt via the drive.

"Gravity is arguably the sole force in play"...... well what about the energy available from the conveyor again?

Quite frankly, I don't suppose Saini needs to get bogged down in all this, as his conveyor does not warrant rocket science, and there has been quite sufficient information given in this thread already.

Cheers

LSL Tekpro ■

I agree with Graham. The discharge is as simple or complex as we care to make it and most of us prefer to stay away from rocket science for these simple projectiles. ■

First, the trajectory does not follow any of the published articles given in MHEA, CEAM, ISO, DIN,.... when the belt velocity is sufficiently slow to allow gravity to overtake the trajectory path per these well meant methods. The methods do not consider the rock charge leaving the pulley may not support the rocks position prior to crossing the pulley centerline.

Observe a horizontal belt feeder in the stopped position with a full charge. Note, the material leaving the pulley has a angle of repose along its lenghtwise axis with charge at the belt line surface and as it slopes backward away from the pulley centerline as it reaches full depth, (ie the repose angle). The same happens with slow motion < 1.5 m/s to varying degrees dependent on feeder speed.

I demostrated this at the Mumbai Bulk Solids conference about 4-5 years ago through the DEM analysis.

It cannot be easily captured without added information on rock size, moisture influence, et al. This I will not attempt. It is easily shown with DEM analysis. ■

Originally Posted by nordell

the trajectory does not follow any of the published articles given in MHEA, CEAM, ISO, DIN,....

How true!

I would have hoped that by now there would have been some significant movement to the preparation of new guidelines on predicted trajectories.

Nice as it would be to use DEM to establish the trajectory, I am suspicious that the costs would be prohibitive for many applications.

Any chance of some cost guidance Lawrence, price of software so we can do it ourselves, price for producing a trajectory if we can't afford the software.?? ■

Let me think on it. We will be producing a whole new BELTSTAT version, quite different from the present issue that can have a functional DEM for the trajectory.

You have got us thinking that this may be a good thing. ■

Alternatively, another good thing might be a "stand alone" DEM trajectory programme. ■

[QUOTE=nordell;49574]

Observe a horizontal belt feeder in the stopped position with a full charge. Note, the material leaving the pulley has a angle of repose along its lenghtwise axis with charge at the belt line surface and as it slopes backward away from the pulley centerline as it reaches full depth, (ie the repose angle). The same happens with slow motion < 1.5 m/s to varying degrees dependent on feeder speed.

QUOTE]

Yes, I agree. This illustrates the static situation.

Attachments

rill angle2 (JPG)

■